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Comparisons of the denoising techniques based on the wavelet shrinkage threshold (WST), general matching pursuit (GMP), and the genetic matching pursuit, so-called (GAMP), are studied in this paper. Using a Matlab program, some typical signals in engineering, such as the true and noisy Blocks, Bumps, Doppler and Quadchirp, are generated and denoised by the WST, GMP and GAMP approaches. Furthermore, denoising effectiveness and accuracy of these methods are discussed. The results suggest that the studied techniques can be used for processing different kinds of signal. The GMP- and GAMP-based methods are more powerful for keeping the high-frequency and suppressing the low-frequency components of the signals, and the WST inverse. The GAMP can save much computation time comparing with the GMP. These conclusions can also be deduced from the denoising application examples performed in the final section of this paper by using some tested stationary and nonstationary engine noise signals.